On turbulent particle fountains

Mingotti, Nicola and Woods, Andrew W. (2016) On turbulent particle fountains. Journal of Fluid Mechanics, 793. ISSN 0022-1120, ESSN: 1469-7645 DOI 10.1017/jfm.2016.167

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Abstract

We describe new experiments in which particle-laden turbulent fountains with source Froude numbers 20>Fr0>6 are produced when particle-laden fresh water is injected upwards into a reservoir filled with fresh water. We find that the ratio U of the particle fall speed to the characteristic speed of the fountain determines whether the flow is analogous to a single-phase fountain ( U≪1 ) or becomes a fully separated flow ( U⩾1 ). In the single-phase limit, a fountain with momentum flux M and buoyancy flux B oscillates about the mean height, hm=(1.56±0.04)M3/4B−1/2 , as fluid periodically cascades from the maximum height, ht=hm+Δh , to the base of the tank. Experimental measurements of the speed u and radius r of the fountain at the mean height hm , combined with the conservation of buoyancy, suggest that Fr(hm)=u(g′r)−1/2≈1 . Using these values, we find that the classical scaling for the frequency of the oscillations, ω∼BM−1 , is equivalent to the scaling u(hm)/r(hm) for a fountain supplied at z=hm with Fr=1 (Burridge & Hunt, J. Fluid Mech., vol. 728, 2013, pp. 91–119). This suggests that the oscillations are controlled in the upper part of the fountain where Fr⩽1 , and that they may be understood in terms of a balance between the upward supply of a growing dense particle cloud, at the height where Fr=1 , and the downward flow of this cloud. In contrast, in the separated flow regime, we find that particles do not reach the height at which Fr=1 : instead, they are transported to the level at which the upward speed of the fountain fluid equals their fall speed. The particles then continuously sediment while the particle-free fountain fluid continues to rise slowly above the height of particle fallout, carried by its momentum.

Item Type: Article
Uncontrolled Keywords: 2016AREP; IA0
Subjects: 05 - Petrology - Igneous, Metamorphic and Volcanic Studies
Divisions: 05 - Petrology - Igneous, Metamorphic and Volcanic Studies
99 - Other
Journal or Publication Title: Journal of Fluid Mechanics
Volume: 793
Identification Number: 10.1017/jfm.2016.167
Depositing User: Sarah Humbert
Date Deposited: 06 Jun 2017 15:46
Last Modified: 06 Jun 2017 15:46
URI: http://eprints.esc.cam.ac.uk/id/eprint/3974

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